Showing papers in "Journal of the Optical Society of America in 1971"

Lightness and Retinex Theory

Abstract: Sensations of color show a strong correlation with reflectance, even though the amount of visible light reaching the eye depends on the product of reflectance and illumination. The visual system must achieve this remarkable result by a scheme that does not measure flux. Such a scheme is described as the basis of retinex theory. This theory assumes that there are three independent cone systems, each starting with a set of receptors peaking, respectively, in the long-, middle-, and short-wavelength regions of the visible spectrum. Each system forms a separate image of the world in terms of lightness that shows a strong correlation with reflectance within its particular band of wavelengths. These images are not mixed, but rather are compared to generate color sensations. The problem then becomes how the lightness of areas in these separate images can be independent of flux. This article describes the mathematics of a lightness scheme that generates lightness numbers, the biologic correlate of reflectance, independent of the flux from objects

Spatial-Frequency Channels in Human Vision*

Abstract: Psychometric functions were determined concurrently for detection of simple gratings (luminance sinusoidally modulated with spatial frequency f) and complex gratings (luminance modulated by the sum of two sinusoids, with frequencies f and f′). Results were used to test the hypothesis that the two components of a complex grating may be detected independently. In an extensive experiment with f = 14 cycles/deg, the independence hypothesis was consistently rejected only when f/f′=54 or 45, but rarely rejected when the value of f/f′ lay outside this range. In other experiments, f was between 1.9 and 22.4 cycles/deg. All results are compatible with the assumption that the human visual system contains sensory channels, each selectively sensitive to different narrow ranges of spatial frequencies, whose outputs are detected independently.

Behavior of the Refractive-Index-Structure Parameter near the Ground*

Abstract: A semiempirical theory is developed which relates the refractive-index-structure parameter Cn2 in the lowest few tens of meters to the vertical gradients of wind speed and temperature and to a stability parameter. This provides an indirect method of determining Cn2, or its temperature counterpart CT2, and the method is successfully applied to recent data which include directly measured CT2 values. The height dependence of the structure parameter is also determined, and the predicted z−4/3 profile under unstable conditions agrees with recent data in the free atmosphere at heights up to 500 m.

Lateral Displacement of Optical Beams at Multilayered and Periodic Structures

Abstract: Many planar structures, including multilayered media and periodic configurations of the optical-grating type, are capable of supporting an electromagnetic field of the leaky-wave form. By exciting this field, an incident light beam transfers a portion of its energy into the leaky-wave structure; after being guided longitudinally for a certain distance along the structure, this energy is leaked back to form part of the reflected beam. Owing to the longitudinal energy flow, the complete reflected beam exhibits a lateral displacement that appears either as a forward beam shift, similar to the Goos-Hanchen effect along a single dielectric interface, or as a backward beam shift, which has not been identified before. By deriving a general expression for the field excited by a gaussian light beam incident upon a leaky-wave structure, we find that the reflected beam may undergo a lateral displacement of the order of the beam width; the magnitude of this beam shift may therefore be much larger than the maximum shift produced at a single dielectric boundary. In the case of periodic structures, all of the higher-order diffracted beams are shifted laterally whenever the specularly reflected beam is displaced. The dependence of the lateral displacement on the beam width, the angle of incidence, and the leakage distance is examined in detail and the relevance of the beam shift to optical-beam couplers is discussed.

Anomalous Stereoscopic Depth Perception

Abstract: Normal or complete stereoscopic depth perception is based upon at least two and probably three mechanisms. These mechanisms may be isolated by studying depth judgments made by stereoanomalous individuals who are unable to discriminate disparities over wide ranges of disparity. The nature of the reductions observed among these stereoanomalous observers suggests that at least three ranges of the disparity are sampled in order to create three different pools of binocular activity. The pools correspond roughly to crossed, near-zero, and uncrossed disparities.

Lateral Displacement of a Light Beam at a Dielectric Interface

Abstract: The lateral (Goos–Hanchen) shift of a gaussian light beam incident from a denser medium upon the interface to a rarer medium is investigated by means of a rigorous integral representation comprising a continuous plane-wave spectrum. By applying a Fresnel approximation to that integral, we derive the lateral displacement for angles of incidence that are arbitrarily close to the critical angle of total reflection. Our results show that, in general, the lateral displacement is a function of the beam width, as well as the incidence angle; the classical expression appears as a limit case which holds only for large beam widths and for incidence angles that are not too close to the critical angle. An analysis of our expression for the beam shift reveals that, as the incidence angle approaches the critical angle of total reflection, the beam shift approaches a constant value that is strongly dependent on the beam width, in contrast to the classical expression, which predicts an infinitely large displacement; we also find that the maximum lateral displacement occurs at an angle that is slightly larger than the critical angle. Numerical results are presented in terms of normalized curves that are applicable to a wide range of realistic beams.

Speckle Removal by a Slowly Moving Diffuser Associated with a Motionless Diffuser

Abstract: A moving diffuser destroys the spatial coherence of laser light only partially when the integration time is finite; this can be expressed by the signal-to-noise (S/N) ratio in the observed illuminance, due to the residual speckle. The method can be improved by the use of a two-diffuser system of which one diffuser is motionless, the other moving. In this case, the integration time (or the displacement of the diffuser) required to obtain a given S/N ratio can be greatly reduced, allowing the use of a slowly moving diffuser. Moreover, the S/N ratio does not depend on the optical-system parameters, whereas it depends on these parameters when a single diffuser is used.

Theory of Flicker and Transient Responses, I. Uniform Fields*

Abstract: Photopic flicker data are explained in terms of a theoretical model of two retinal processes. The first is a linear diffusion process (presumably in the receptors), with a large dynamic range (∼105). The second is a nonlinear inhibiting network (neural feedback at the synapses of the plexiform layers) that adaptively controls the sensitivity and time constants of the model. The magnitude of its transfer function fits the flicker data quantitatively at all frequencies, over a wide range of adaptation levels. The corresponding small-signal impulse responses are also calculated: their latencies and leading edges (associated with receptor activity) are invariant with adaptation level; the remaining phases of these transient waveforms (associated with the graded potentials of secondary neurons) adapt strongly, in accord with current histology and micro-electrode findings.

Theoretical Eye Model with Aspherics

Abstract: A model for the human eye is proposed, similar to Gullstrand’s well-known 4-radius model, however with the front surface of the cornea and the back surface of the crystalline lens taken to be rotationally symmetric aspherics. Whereas for the cornea a polynomial is used based on experimental data of Bonnet, a second-order parabola was tentatively adopted for the back surface of the lens. This model results in slight spherical undercorrection, in agreement with experimental findings. On the other hand, the sine condition is not well satisfied, probably due to neglect of the shell structure of the lens. By ray tracing, astigmatism and coma as well as the meridional and sagittal focal lengths were computed up to a visual angle of 90°. Calculations were also made for the same model preceded by a plano-concave contact lens (Goldmann 3-mirror contact glass), showing that this combination results in considerably reduced astigmatism.

Modified Kramers–Kronig Analysis of Optical Spectra

Abstract: A modified Kramers–Kronig integral is derived, which offers greater convergence than the conventional expression when reflectance data are available over a limited range. The modified expression produces good convergence when applied to synthetic spectra.

Complex Rays with an Application to Gaussian Beams

Abstract: The use of rays to construct fields is illustrated by finding the field in the region z>0 when the field is given on the plane z = 0. This construction is valid for complex rays as well as real ones. The method is applied to a gaussian field in the plane z = 0, in which case a gaussian beam results. The calculation involves only complex rays. Exactly the same results are also obtained by applying the method of stationary phase to an integral representation of the field. However, the ray method is simpler than the stationary-phase method, and it is also applicable to problems for which the stationary-phase method cannot be used because no integral representation of the field is known.

Theory of Flicker and Transient Responses,* II. Counterphase Gratings

Abstract: The model derived in the preceding paper is applied to new sine-wave flicker data, obtained with 7° circular, uniform-field and counterphase-grating targets, at four adaptation levels ranging from 1.67 to 1670 td. The data from all eight conditions are well fitted by varying two parameters associated with neural-inhibition processes; the major effect of changing the spatial pattern is on the number of neural units involved. But even when lateral inhibition is minimized, low-frequency feedback still dominates the transient responses of the model. These results can be interpreted in terms of spatial and temporal filtering in the outer and inner plexiform layers of the retina.

Optical Constants of Water in the Infrared

Abstract: The infrared reflectance of water in the region 5000–300 cm−1 has been measured at near-normal incidence and at an incidence angle of 53°. On the basis of the measured values of spectral reflectance and the existing data on spectral transmittance, we have obtained values for the real and imaginary parts of the refractive index of water. The resulting values, which are presented in both graphical and tabular form, are compared with recent determinations by other investigators.

Energies of the Electronic Configurations of the Singly, Doubly, and Triply Ionized Lanthanides and Actinides

Abstract: Methods are described for estimating energies of the electronic configurations of the gaseous ions of the lanthanides and actinides. Energies are tabulated for the lowest spectroscopic level of the configurations involving 4f, 5d, 6p, and 6s electrons for the lanthanide ions and 5f, 6d, 7p, and 7s electrons for the actinide ions. Some additional values are listed to be added to the previous tabulation for neutral atoms.

Energies of the Electronic Configurations of the Lanthanide and Actinide Neutral Atoms

Abstract: The thermodynamic data for the lanthanide and actinide metals have been combined with spectroscopic data to develop a method of estimating the energies of the electronic configurations of the neutral gaseous atoms. Energies are tabulated for the lowest spectroscopic level of each configuration. Many of the odd terms of La i have been reclassified.

Lambert Absorption Coefficients of Water in the Infrared

Abstract: By use of a wedge-shaped cell providing an absorbing layer tapering in thickness from less than one wavelength of visible light at one end to approximately 20 μm at the other end, we have measured the Lambert absorption coefficient for water in the spectral region between 4000 and 288 cm−1. After proper initial alignment of the cell windows had been established by the observation of interference fringes in the visible, we measured film thicknesses at various positions along the wedge by interferometric methods, employing convenient wavelengths in the infrared. We present the results of the study in graphical and tabular form.

New Color-Matching Ellipses

Abstract: Three new sets of color-matching experiments have been made by three observers binocularly viewing a bipartite field (each half subtending 3°) of a three-primary colorimeter. Each set of color-matching data refers to 28 test colors scattered over the chromaticity gamut provided by the colorimeter. The luminance of each test color was 12 cd · m−2; the white surround (subtending 40°) was maintained at 6 cd · m−2. The elliptical cross sections (for Y = const) of the observed color-matching ellipsoids are compared with results previously published by MacAdam, and Brown and MacAdam. In view of the inherent experimental uncertainties of data of this kind, the new color-matching ellipses correlate well with those obtained by Brown, and Brown and MacAdam, but show significant deviations from those obtained by MacAdam’s observer P. G. Nutting, Jr. The discrepancies are puzzling. A note of caution is added with regard to the usefulness of color-matching ellipses in testing line elements. A set of color-matching ellipses can reveal only little of the visual mechanism that governs the precision of color matching and its assumed direct correlation with judging small color differences. It appears that fundamentally different line elements can reproduce almost equally well a given set of color-matching ellipses.

Luminosity and Color-Rendering Capability of White Light

Abstract: The spectral power distribution of white light required to maximize luminous efficiency and the color-rendering index is approximated by additive combination of three spectral lines near 450, 540, and 610 nm. The two wavelength regions near 500 and 580 nm are disadvantageous. These results are related to the color-mixture functions of human color vision. Three functions that indicate the effectiveness of red, green, and blue light for composing high-performance white light are shown.

Ellipsometry of Anisotropic Films

Abstract: The macroscopic description of the optical behavior of (thin) films adsorbed on a polished solid surface is extended by allowing for uniaxial anisotropy in the adsorbate. The theoretical results are applied to Langmuir–Blodgett layers of absorbing and nonabsorbing surface-active compounds.

Temporal-Frequency Spectra for a Spherical Wave Propagating through Atmospheric Turbulence

Abstract: Tatarski has found the frequency spectra for the amplitude, phase, and phase-difference fluctuations of an infinite plane wave propagating through turbulence. Many practical optical beams, used in atmospheric studies, closely resemble point sources, for which the spherical-wave theory is more applicable. The same spectra, calculated for spherical waves, reveal contributions at higher frequencies for amplitude scintillations, nearly identical phase results, and a phase-difference spectrum with no nulls, in contrast with the plane-wave results. Comparison with recent data is shown.

Phase-Only Complex-Valued Spatial Filter*

Abstract: A new type of phase-only filter is described for wave-front construction, in which both the amplitude and phase information necessary to construct an arbitrary image over a limited field are encoded. It is shown that this phase-only filter can duplicate the performance of an ideal complex-valued spatial filter (a filter that controls both amplitude and phase transmittance). This phase-only filter controls the amplitude transmittance by the use of a modulated high-frequency phase carrier that diffracts a controlled amount of light into the image. This type of filter is particularly useful in the implementation of computational wave-front construction, because the maximum spatial frequency that must be plotted is associated with the image and not the carrier. The performance of the filter is examined both numerically and experimentally.

Reciprocity of the Turbulent Atmosphere

Abstract: The reciprocity theorem of Helmholtz is extended to the clear turbulent atmosphere. Two impulse responses (Green’s functions) are defined to characterize optical propagation in opposite directions between two parallel planar apertures separated by the turbulent atmosphere. It is shown that these impulse responses satisfy the same reciprocity condition as the free-space impulse responses do. This result underlies recent studies of adaptive communication systems for the turbulent channel.

Optimum Excitation of Optical Surface Waves

Abstract: The theory of the prism–film coupler is generalized to include cases in which the thicknesses of both the coupling gap and of the light-guiding film vary along the direction of propagation. The profiles of gap and film are optimized with respect to the input beam, resulting in a theoretical coupling efficiency of practically unity. It is shown that the problem of optimum coupling is equivalent to the problem of matching the spatial amplitude distribution of the input beam to the leakage field of the coupler. This theory is applied to a coupler with a linearly tapered gap, yielding a theoretical coupling efficiency of 0.96. Experimentally, an efficiency of 0.88 has been achieved.

Wave Structure Function and Mutual Coherence Function of an Optical Wave in a Turbulent Atmosphere

Abstract: The most commonly used expression for the wave structure and mutual coherence function for an optical wave propagating in a turbulent atmosphere, which is based on an unphysical extrapolation of the Kolmogorov spectrum, is shown in general to be incorrect. For a modified spectrum, we show that the correction to the wave structure and mutual coherence functions, the implied resolution, and the resulting signal-to-noise (S/N) ratio using heterodyne detection, are considerable. Approximate expressions for the coherence function, valid over three distinct propagation distance regions, are derived, and experimental evidence in support of our results is cited.

Scattering of Light from a Rotating Ground Glass

Abstract: We report some experimental results concerning the statistical properties of a light beam scattered by a rotating ground glass with average-size inhomogeneities of approximately 1 μm. Photocount statistics measured at different scattering angles and for different angular velocities of the ground glass have confirmed the known result that the scattered-light amplitude is a stochastic gaussian variable. The Bose–Einstein nature of the photocount statistics has been verified with an accuracy of a few parts per thousand. Self-beating measurements on the scattered light of a He–Ne laser in a TEM00 configuration have shown that the power spectrum is a gaussian function of the frequency. The dependence of its half-width on the angular velocity of the ground glass and on the focal length of the lens that focuses the beam on the scattering surface has been measured. The experimental results agree very closely with our theoretical predictions.

Enhancement of absorption spectra by dye-laser quenching

Abstract: Absorption spectra enhancement by organic dye laser quenching, considering applications for absorbing species spectroscopic detection

Simultaneously recorded retinal and cortical responses to patterned stimuli.

Abstract: The method of stimulus alternation was used to record simultaneously electroretinograms (ERGs) and visually evoked cortical potentials (VECPs) to stimuli of differing luminance and pattern. Stimuli consisted of checked and striped patterns with a variety of spatial frequencies. ERGs of approximately equal amplitudes were elicited by patterns of the same spatial frequency regardless of pattern. ERG amplitude decreased monotonically with increasing spatial frequencies of the patterns. Simultaneously recorded VECPs were consistently larger for checked patterns than for striped patterns of equal spatial frequency. The largest VECPs were seen with checked patterns having spatial frequencies of approximately 1 cycle/deg of visual angle: frequencies both higher and lower than this value produced smaller responses.

Pauli-Algebraic Operators in Polarization Optics*

Abstract: Techniques for analysis and synthesis of linear optical systems involving polarization effects are related and extended through fuller exploitation of the algebra of complex 2 × 2 matrices.

Parameter-Correlation and Computational Considerations in Multiple-Angle Ellipsometry*

Abstract: An absence of correlation between parameters, indicated by invariance of the normalized ratio of the first derivatives of Δ, makes it possible to make optimal use of the overdetermined set of equations, which are available from multiple-angle measurements. Accurate estimates of the parameters are not needed for the correlation test so that experimental conditions can be chosen to minimize correlation. Also, the second derivatives of the least-squares residuals are useful in deciding on the best method of searching for a solution, in error analysis and in illustrating the critical importance of initial estimates of the unknown parameters in obtaining accurate least-squares solutions.